How far in advance to make restaurant reservations in Rome and in smaller cities?

It's pretty much the same as the US in that it depends on the popularity of the restaurant. For many smaller places, especially outside big cities, they may only answer the phone near service hours, so calling the same day around lunch or on the evening prior for an evening dinner would usually work. For a busy time slot, say Sunday lunch at a good country place, you should call a couple of days ahead.

Yes, call or stop by during open hours the day before for a lunch reservation, or be prepared to eat at your second or third choice (which may be just great, too!). We have had mixed results booking online, emailing, or using Whatsap.

For lunch in Orvieto:

Labirinto Di Adriano (our favorite during our 4 night stay)

Trattoria la Palomba

Il Malandrino Bistrot

La Pergola

In most cases the same day is enough.
Some super busy restaurants may be booked on certain days (weekends).

If it helps, we rarely make reservations, if we do, it is after seeing the place and the menu, and then usually only the day of, maybe the day before.

Of course, I am always leery of a place "seen on TV", and have no attraction to Michelin stars, so never looking to lock something in weeks and months in advance.

Thanks! I’m not looking for reservations at places seen on TV but several people on the forum have recommended small restaurants in particular cities and said an advance reservation was needed. I’d like to mix it up with a few places reserved in advance and others recommended on site or that we happen upon.
I’d also like to have at least one dinner in Rome reserved in advance at a restaurant others have recommended.

We travelled with a group of six last summer and were able to make reservations either the day before or same day for dinner. It helps if you want to eat early (7:30 or 8).

I like to have a reservation on my arrival night in each city, so I’m not searching for a place after a travel day.

It’s easier with a smaller group. Often my husband and I would arrive at a restaurant right when they open, and the outside tables all had reserved signs. When we asked, they would say, “We can seat you but you must be done by 8:30 because the table is reserved at that time.” I think Americans are known for eating fast, unlike locals who may linger for hours.

If it's just a party of two, they should be able to sit you even without reservations, almost anywhere.

Reservations might be worthwhile in May. Do you have "wandering time" in your schedule? Maybe use it to scout out interesting places to eat. I'd base 'interesting' on the number of languages used on the displayed menu (the more, the more I avoid the place), the perceived atmosphere and attitude of the customers and wait staff. Prices matter - sometimes you want to splurge, sometimes you don't. If the place looks interesting enough, make a reservation for the best night and time available. Keep a list! The last thing you want to accept is: "we can sit you early but you have to be done by a certain time". The food may be good but you would be missing out on one of the great cultural experiences of Italy: leisurely meals! Make finding good, fun, interesting, popular places to eat part of the vacation!